Operation Charybdis was a joint Special Activities Division and MI-6 operation to eliminate Jason Hudson, Grigori Weaver, and Alex Mason, to be taken place in 1978, 10 years after the events of Call of Duty: Black Ops. 
The primary goal was to terminate Mason, whom the S.A.D. deemed to be mentally unstable and became a threat to national security; Hudson and Weaver were also included as targets for termination due to their backing of Mason, thereby making them a threat to national security as well.
Although it is known that CIA analyst Ryan Jackson will join the task force as adviser (due to his extensive knowledge of the targets, given he handled the reports and analysis of personnel and events concerning the trio) along with a young Special Air Service operator named Jonathan, nothing is known about the outcome of the mission or the fate of its participants because, as of 30 October 1978, the operation was still in the preparation phase, with Ryan Jackson's temporary field operative status only having been approved days before.
It can be assumed that the mission either failed or was dissolved as the events from Call of Duty: Black Ops II show Hudson, and Alex Mason (and Mason's son who was born in 1979) to be alive, after the Operation was to take place, and Hudson still operated for the CIA, using Alex Mason along with him and Frank Woods. The fate of Grigori Weaver, however, is not known.
- In a separate email to Ryan Jackson, his supervisor, Richard Kain, warned Jackson not to let this Operation be disclosed to other CIA staff, because Hudson has many friends in the agency and this operation would surely be unpopular.
- In Ryan Jackson's database there's a CIA dossier concerning one CIA's double agent, a GRU operative named Kristina. Her current GRU assignment, as of 1978, was to track down and capture Mason. Thus, the report suggested to recruit her as operational asset for the mission.
- According to a message from Hudson to Mason, it is likely that they went to Johannesburg, to search for an unknown lead. Doctor Clarke had a brother in Johannesburg who he intended to hide with, according to intel obtained in "Numbers".
- In Black Ops II, on the level Suffer with Me; Mason said a line that is related to the Operation, "Wait on Hudson's go. The CIA is watching his every move."